TikZ braids package: inserting identities/space in braid diagrams

Assuming that you don't want to enlarge the height of all groups I think you need a "dummy" strand. Be aware that it changes the bounding box of the graphic, so you need to adapt it.

\documentclass[a4paper]{scrartcl}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\usepackage{braids}

\begin{document}

\begin{tikzpicture}
\braid[number of strands=4,
       style strands={5,6}{draw=none}] (braid) a_2 a_3 a_5 a_5 a_5 a_3 a_2;
\end{tikzpicture}


\end{document}

The version of braids that is available on github introduces the symbol 1 to the braid word, meaning that it is possible to specify a segment with no crossings whatsoever.

Taking Ulrike's example, this could be rewritten as:

\documentclass[a4paper]{scrartcl}

\usepackage{tikz}
\usepackage{braids}

\begin{document}

\begin{tikzpicture}
\braid a_2 a_3 1 1 1 a_3 a_2;
\end{tikzpicture}


\end{document}